messages listlengths 1 1 | ground_truth stringlengths 1 7 | dataset stringclasses 1
value |
|---|---|---|
[
{
"content": "What is the value at position (3, 5) of the matrix A^4 where A is:\n[[-2, -5, -5, -2, -1],\n [1, -2, 4, -5, 5],\n [4, 1, -4, 5, -4],\n [2, 4, 4, 4, -1],\n [4, -4, -1, 2, 0]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -125 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[-3, 2, 3, -1, -4],\n [-4, 1, -5, 4, -4],\n [4, -2, -5, -2, 5],\n [4, -1, 3, -5, -1],\n [-4, 3, 0, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -11515 | MATH |
[
{
"content": "Find the sum of all entries of the 4th power of the matrix:\n[[2, -5, -3, 4, -5],\n [5, 5, 2, -5, -1],\n [-2, 1, -1, 2, 5],\n [-5, -1, -2, -3, -1],\n [4, -3, 2, -3, -5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 4507 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[3, 2, 0, 1, 0],\n [2, -4, 3, 0, 0],\n [0, 3, -5, 4, -2],\n [1, 0, 4, 3, -2],\n [0, 0, -2, -2, -5]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 202730 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[4, 1, -2, 2, -3],\n [-5, -1, -4, -3, 0],\n [-3, -3, 0, -1, 4],\n [3, -5, -3, -3, 5],\n [0, 2, -3, -3, 0]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 72819 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[2, 0, 4, -3, -2],\n [-5, 2, -2, 0, 5],\n [-3, 5, 5, 0, 5],\n [3, 3, 4, -3, -3],\n [-2, 1, -3, 4, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 29109 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[5, 2, 0, -2, 5],\n [5, -1, -4, 0, -3],\n [0, -1, -4, -1, -1],\n [3, 5, 2, 1, -3],\n [4, -2, 0, -3, 5]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 32496 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[3, 4, -2, -3, 1],\n [4, -3, 4, 3, -3],\n [-2, 4, -1, 0, 3],\n [-3, 3, 0, -1, 2],\n [1, -3, 3, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2446 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-2, 2, -5, -2, 0],\n [-2, 0, -1, 3, 4],\n [3, -2, -2, 2, 4],\n [-2, -4, -4, -5, -1],\n [0, 3, -1, 0, 0]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 12271 | MATH |
[
{
"content": "Find the value at position (1, 2) of the 4th power of the matrix:\n[[-3, -2, -3, 0, 0],\n [-2, 5, 4, 4, -2],\n [-3, 4, -4, -1, -1],\n [0, 4, -1, -1, 2],\n [0, -2, -1, 2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1342 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[2, 0, 5, 0, -4],\n [0, 5, 2, 2, -2],\n [5, 2, -4, 0, -4],\n [0, 2, 0, -5, 0],\n [-4, -2, -4, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 67152 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-5, 2, 5, 3, 2],\n [2, -1, -1, -1, -1],\n [5, -1, 2, 1, -1],\n [3, -1, 1, 4, 4],\n [2, -1, -1, 4, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 13991 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (2, 4) of the result:\nA =\n[[0, -3, 5, 4, 2],\n [1, -5, 4, -1, 4],\n [3, 5, 0, 2, 4],\n [-5, 4, 5, 1, -3],\n [3, 0, -1, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 696 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-3, -2, 0, -2, 2],\n [-2, 2, 4, -2, 2],\n [0, 4, -3, 1, -4],\n [-2, -2, 1, 5, 2],\n [2, 2, -4, 2, 4]], determine the value at position (2, 5).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1068 | MATH |
[
{
"content": "What is the value at position (2, 1) of the matrix A^5 where A is:\n[[1, 1, 0, 1, -4],\n [1, -4, 1, 0, -2],\n [0, 1, 3, 4, 2],\n [1, 0, 4, 5, 0],\n [-4, -2, 2, 0, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1617 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[4, -3, 5, -3, -5],\n [4, -5, 0, -5, -1],\n [-2, -1, 1, 0, 3],\n [0, 3, -2, -5, -5],\n [4, 1, -3, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 14776 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[0, 1, -1, 2, 1],\n [-4, -5, 3, -1, 5],\n [-1, 4, -2, -4, -1],\n [-4, 1, 5, 3, 3],\n [5, 0, -5, 0, -1]], determine the value at position (5, 5).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -5601 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-2, 0, 0, 1, 0],\n [0, -2, 0, 2, 0],\n [0, 0, 3, -1, 0],\n [1, 2, -1, 5, 4],\n [0, 0, 0, 4, -5]], determine the value at position (3, 4).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -471 | MATH |
[
{
"content": "Find the value at position (4, 4) of the 5th power of the matrix:\n[[-5, -4, 4, 4, -1],\n [-2, -5, -2, -2, 4],\n [-2, -5, 3, -3, -2],\n [-1, 1, 0, -1, 2],\n [-5, 1, 0, 5, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 438 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (3, 2) of the result:\nA =\n[[1, 0, -4, 0, -1],\n [0, -3, 1, 2, 1],\n [-4, 1, 1, -2, 0],\n [0, 2, -2, -2, 2],\n [-1, 1, 0, 2, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -222 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[-5, 1, 0, -4, 5],\n [1, 0, -1, 2, -1],\n [5, -4, 0, -5, -1],\n [0, 1, -4, -5, 0],\n [-3, -1, 5, -4, -5]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -57409 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[-5, 5, -2, 4, -4],\n [-5, 0, -2, 4, 1],\n [5, 0, -1, 4, -4],\n [-1, 3, 3, -4, 1],\n [4, -2, -3, 5, -5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 359785 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-3, 5, 3, 3, 1],\n [-3, -3, -2, 1, 1],\n [-4, -1, 1, 1, 0],\n [4, 4, 2, -3, -5],\n [-3, 5, -4, -4, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1654 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the sum of absolute values of all entries of the result:\nA =\n[[-1, -3, 3, -4, 0],\n [-3, -4, -3, 4, 2],\n [3, -3, -1, 4, 0],\n [-4, 4, 4, -2, -2],\n [0, 2, 0, -2, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 581797 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[1, -4, -5, 0, 0],\n [4, -4, -5, 4, -3],\n [4, -1, 0, -3, 3],\n [5, -1, -4, 4, 0],\n [2, 5, 0, -2, 0]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3080 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the sum of all entries of the result:\nA =\n[[2, 1, 4, 0, -1],\n [1, -4, -3, -1, 1],\n [4, -3, 4, 2, 4],\n [0, -1, 2, 2, 0],\n [-1, 1, 4, 0, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 109328 | MATH |
[
{
"content": "What is the value at position (1, 5) of the matrix A^5 where A is:\n[[-2, -3, -2, 4, 1],\n [4, 2, -5, 2, -1],\n [1, 5, 5, -5, -4],\n [-5, -1, 0, 4, 3],\n [2, 1, -1, -3, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -7180 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-1, -4, -2, 0, 2],\n [-4, 5, -3, 0, -3],\n [-2, -3, -4, 2, 2],\n [0, 0, 2, -3, -2],\n [2, -3, 2, -2, -3]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 30552 | MATH |
[
{
"content": "Find the value at position (5, 2) of the 4th power of the matrix:\n[[2, -1, -2, 0, 4],\n [-1, 1, 1, -2, -1],\n [-2, 1, -3, -2, 2],\n [0, -2, -2, -5, 3],\n [4, -1, 2, 3, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -932 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-1, 0, 4, -4, -4],\n [0, -1, 0, 4, -2],\n [4, 0, 3, 4, 0],\n [-4, 4, 4, -5, -2],\n [-4, -2, 0, -2, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 13381 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[4, -2, 0, -2, -2],\n [-2, 5, -2, 1, 0],\n [0, -2, -2, 4, 0],\n [-2, 1, 4, -4, -4],\n [-2, 0, 0, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 324742 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[-3, -4, -1, 4, -3],\n [-3, 2, -2, -2, -3],\n [5, -5, 2, -5, 1],\n [-1, -2, -2, 2, 5],\n [5, 0, -5, 4, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 32055 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the sum of absolute values of all entries of the result:\nA =\n[[-4, 1, 1, -1, 1],\n [1, 4, -4, 2, 0],\n [1, -4, -2, 2, 1],\n [-1, 2, 2, -4, 0],\n [1, 0, 1, 0, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 101840 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[3, 0, 0, 0, 4],\n [0, -1, 2, -2, -2],\n [0, 2, -1, 0, 0],\n [0, -2, 0, 3, 0],\n [4, -2, 0, 0, -1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 7383 | MATH |
[
{
"content": "Find the sum of all entries of the 5th power of the matrix:\n[[-4, -2, -4, -3, 4],\n [-3, -2, 0, -3, 4],\n [-5, -5, 3, 3, -1],\n [3, 5, 1, 3, 1],\n [3, -4, 5, 5, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -19196 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[1, -2, -2, -2, 0],\n [-2, 2, 0, -2, 5],\n [-2, 0, -1, 0, 0],\n [-2, -2, 0, 2, -2],\n [0, 5, 0, -2, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 9447 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[3, 1, 0, 0, -4],\n [1, 3, -4, -2, 4],\n [0, -4, -5, 3, 1],\n [0, -2, 3, -2, -2],\n [-4, 4, 1, -2, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 279773 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[-5, 3, 2, 2, -1],\n [3, -2, 2, 4, 1],\n [2, 2, 4, -2, 0],\n [2, 4, -2, 2, -2],\n [-1, 1, 0, -2, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 9932 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[1, 3, -3, 4, -2],\n [4, -2, 4, -1, 0],\n [-3, -2, -3, -4, 4],\n [3, -5, -4, 2, 1],\n [-5, -1, 4, 0, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 243451 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[-2, -4, -2, 0, 0],\n [-4, 4, -2, 4, 2],\n [-2, -2, -5, 0, 0],\n [0, 4, 0, 1, 2],\n [0, 2, 0, 2, 0]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 225814 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[-1, -4, 2, 1, 0],\n [-1, -1, 3, -5, 3],\n [0, -2, 4, 1, 3],\n [-1, -1, 2, 1, 2],\n [5, 4, -4, 3, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 84918 | MATH |
[
{
"content": "Find the sum of all entries of the 5th power of the matrix:\n[[0, 2, -4, 0, 2],\n [2, 5, -2, 2, -2],\n [-4, -2, -4, -2, 1],\n [0, 2, -2, 4, -3],\n [2, -2, 1, -3, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -3754 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-4, -2, 4, 3, 4],\n [3, -2, 3, -3, -1],\n [4, 3, 0, -3, 4],\n [3, 0, -2, -2, 2],\n [1, -5, 0, 2, -3]], determine the value at position (4, 2).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1548 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[3, 4, -4, -2, -5],\n [4, -4, 1, -5, 2],\n [-4, 1, 4, 4, -4],\n [-2, -5, 4, -2, -2],\n [-5, 2, -4, -2, 1]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 71780 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[4, 3, 1, -5, 2],\n [2, -2, 2, -2, 2],\n [-1, -2, 0, -4, -4],\n [-4, 3, 4, -3, 4],\n [-2, 4, 2, -2, 5]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5515 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the sum of absolute values of all entries of the result:\nA =\n[[4, 4, 1, -1, 3],\n [-2, -3, -4, -5, 5],\n [0, 4, -4, 2, 0],\n [-1, -4, 1, -4, -1],\n [-4, 5, 4, 5, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 225420 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[-4, 0, 2, -2, -1],\n [0, -4, -1, -2, 0],\n [2, -1, -3, -1, 0],\n [-2, -2, -1, 1, -2],\n [-1, 0, 0, -2, 3]], determine the value at position (4, 5).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1182 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the value at position (5, 5) of the result:\nA =\n[[-3, -5, 4, 0, -5],\n [-5, 2, 3, -4, 3],\n [-1, 2, 1, 1, -2],\n [-4, -1, 5, 5, -3],\n [3, 0, -5, -3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -2836 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (3, 2) of the result:\nA =\n[[3, 5, 0, -2, -5],\n [2, 5, -4, 5, 5],\n [2, 0, 2, 0, -1],\n [-1, 4, 4, 5, 2],\n [1, 2, 2, 1, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 451 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the sum of absolute values of all entries of the result:\nA =\n[[5, 3, 2, 2, -2],\n [3, -5, 1, -1, 0],\n [2, 1, 5, 0, -2],\n [2, -1, 0, -5, 0],\n [-2, 0, -2, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 320609 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[2, -3, 1, -3, -2],\n [3, -2, -3, -1, 1],\n [-1, -2, 2, -2, -4],\n [4, 0, -4, -3, -5],\n [-1, 3, -4, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5309 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[-4, 2, 5, 0, -2],\n [-2, -4, -3, 1, -3],\n [-1, 4, 0, 0, -2],\n [0, -3, 1, 1, -2],\n [-4, 5, 1, -3, -5]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 87515 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[-4, 2, -1, 4, -2],\n [2, -5, -1, -2, -4],\n [-1, -1, 1, -4, 0],\n [4, -2, -4, 4, -5],\n [-2, -4, 0, -5, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}... | 68876 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-2, 2, -2, -2, 2],\n [2, 0, 0, -2, -3],\n [-2, 0, -3, -3, -2],\n [-2, -2, -3, 1, 0],\n [2, -3, -2, 0, -4]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 13762 | MATH |
[
{
"content": "What is the value at position (2, 3) of the matrix A^4 where A is:\n[[0, 5, -1, 2, 5],\n [-4, -5, 1, 0, 2],\n [5, 2, -4, 2, 0],\n [3, 1, -4, 2, 3],\n [1, -2, 3, -2, -2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 732 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[3, 2, -2, 2, 2],\n [2, 4, -1, 0, 0],\n [-2, -1, -4, 2, 1],\n [2, 0, 2, -1, -3],\n [2, 0, 1, -3, 2]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 20875 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[2, 1, -2, -4, -2],\n [1, 3, -3, -2, 2],\n [-2, -3, 0, 0, -1],\n [-4, -2, 0, -4, 0],\n [-2, 2, -1, 0, 3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -30266 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[3, 0, 0, -3, -3],\n [0, 4, 0, 2, -2],\n [0, 0, -3, 0, 0],\n [-3, 2, 0, 2, 0],\n [-3, -2, 0, 0, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 5214 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[3, -4, -1, -5, -2],\n [-4, 2, -2, -1, 5],\n [-2, -1, -1, -1, 5],\n [-3, 1, -3, -4, -3],\n [5, -3, 2, -2, -3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8459 | MATH |
[
{
"content": "Find the value at position (2, 5) of the 4th power of the matrix:\n[[4, -1, -2, 3, 2],\n [5, 1, 2, -1, -2],\n [1, -5, 0, 2, 1],\n [-4, 1, 0, -1, -2],\n [-5, -4, 1, 4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -362 | MATH |
[
{
"content": "Find the value at position (4, 4) of the 5th power of the matrix:\n[[-1, 2, 2, 0, -1],\n [-4, 3, -5, 5, -4],\n [-5, -2, -2, -1, -1],\n [2, 5, 5, -3, 0],\n [-3, -4, 2, -5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 12255 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[5, -1, 4, 0, 1],\n [-1, 0, 1, 1, -3],\n [4, 1, 5, -1, 0],\n [0, 1, -1, 2, -2],\n [1, -3, 0, -2, 1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 12891 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[2, -2, 5, 2, 1],\n [-2, -2, 0, 0, -3],\n [5, 0, -2, 0, 2],\n [2, 0, 0, 5, 2],\n [1, -3, 2, 2, 3]], determine the value at position (5, 2).\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -587 | MATH |
[
{
"content": "Find the sum of all entries of the 5th power of the matrix:\n[[5, 4, 4, 0, -2],\n [4, -1, -2, -2, 2],\n [4, -2, -5, 4, -2],\n [0, -2, 4, 2, 0],\n [-2, 2, -2, 0, 1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 38136 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the value at position (1, 5) of the result:\nA =\n[[5, 0, 5, 0, -4],\n [-1, -3, 1, -2, -5],\n [0, 0, 1, 5, 2],\n [-3, 0, 4, -4, 3],\n [-4, -3, 4, -4, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1929 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[-5, -1, -5, -1, 2],\n [2, 5, 2, -4, 2],\n [-1, -5, 1, 0, -1],\n [-5, -5, 0, 4, 1],\n [4, 4, -5, 3, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 378030 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[-1, -4, 2, 3, 0],\n [-4, 3, -2, -1, 0],\n [2, -2, 4, -1, 0],\n [3, -1, -1, -4, 0],\n [0, 0, 0, 0, -5]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 15357 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the value at position (4, 5) of the result:\nA =\n[[1, 0, 4, 2, 2],\n [0, -3, 0, 1, -2],\n [4, 0, 0, -2, -4],\n [2, 1, -2, 1, -2],\n [2, -2, -4, -2, 4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -5128 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 5th power of the matrix:\n[[3, -1, -2, -3, 0],\n [-1, 3, -2, 1, -2],\n [-2, -2, 4, 0, -4],\n [-3, 1, 0, 0, 1],\n [0, -2, -4, 1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 68551 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (2, 3) of the result:\nA =\n[[-1, 0, -2, 2, -1],\n [0, -4, 2, 2, -1],\n [-2, 2, -3, 2, 3],\n [2, 2, 2, 2, 2],\n [-1, -1, 3, 2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -952 | MATH |
[
{
"content": "Find the sum of all entries of the 5th power of the matrix:\n[[5, -5, -4, 5, -4],\n [1, 0, 5, -4, 2],\n [3, 1, -2, -5, -2],\n [-2, 2, -2, -2, -4],\n [4, 1, -2, 5, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 29396 | MATH |
[
{
"content": "Find the value at position (4, 4) of the 4th power of the matrix:\n[[-3, 2, 2, -2, 2],\n [2, -1, 4, -1, -3],\n [2, 4, 1, -3, -1],\n [-2, -1, -3, 5, 2],\n [2, -3, -1, 2, 2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3629 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[5, 1, 0, 5, -1],\n [1, 4, 1, 4, -2],\n [0, 1, 2, 4, 1],\n [5, 4, 4, 3, 0],\n [-1, -2, 1, 0, 1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 796152 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[3, 4, 4, -4, 0],\n [0, 3, 3, -1, -1],\n [3, 2, 1, 2, 0],\n [-3, 1, 2, 2, -5],\n [1, -3, -4, -4, 2]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 27201 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[3, -3, -3, 0, 5],\n [4, -5, 0, -3, 5],\n [-2, 3, -3, -5, -3],\n [1, 1, 5, -1, -5],\n [5, 2, 4, 2, 4]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 26754 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[4, 4, -4, 4, -3],\n [-2, -5, -2, -1, -3],\n [5, 4, -4, 0, 2],\n [1, 5, -5, -2, -3],\n [0, 3, 3, 1, 3]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 41009 | MATH |
[
{
"content": "For the matrix power A^4 where A =\n[[2, -1, 3, 1, -1],\n [2, 1, 3, 4, -5],\n [3, 1, -5, -5, -1],\n [2, 3, 0, 4, 2],\n [0, 5, 0, -2, 5]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 14433 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[-1, -2, 0, -4, 3],\n [-2, -1, -2, 1, 0],\n [0, -2, -2, -2, 0],\n [-4, 1, -2, -4, 4],\n [3, 0, 0, 4, -2]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 412614 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of all entries of the result:\nA =\n[[-5, -2, 0, 0, 4],\n [-2, -1, 1, 4, -2],\n [0, 1, -2, -1, -2],\n [0, 4, -1, -2, -2],\n [4, -2, -2, -2, -2]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 558 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^5 where A is:\n[[2, -3, 4, 0, 0],\n [3, 3, -2, 3, 0],\n [-4, 4, 5, 0, -4],\n [2, -2, -1, 2, 5],\n [2, 0, -2, -5, 1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 18782 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[2, 3, -4, -5, -2],\n [-1, 4, -5, -1, 0],\n [-3, 1, 0, -2, -3],\n [-1, -3, 4, 3, 3],\n [0, 5, 0, -2, -2]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -6947 | MATH |
[
{
"content": "What is the value at position (1, 3) of the matrix A^4 where A is:\n[[-4, 0, 2, 2, 4],\n [0, 3, -2, -2, -1],\n [2, -2, 1, -2, 2],\n [2, -2, -2, 5, -2],\n [4, -1, 2, -2, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -218 | MATH |
[
{
"content": "Calculate the matrix power A^5 and find the value at position (2, 4) of the result:\nA =\n[[3, -3, -2, 1, 4],\n [2, 2, -2, 1, 4],\n [-5, 0, 0, 0, -4],\n [2, -1, -1, -4, -2],\n [3, 3, 0, 5, 3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 8723 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[-2, 5, -5, -4, -5],\n [2, 3, 4, 0, -4],\n [0, 3, -3, 3, -4],\n [5, -1, 5, -4, 1],\n [5, 4, 3, 1, -1]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 28893 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[-2, 1, 2, 3, 2],\n [1, 4, 0, 3, -2],\n [2, 0, 5, 2, 2],\n [3, 3, 2, 3, 2],\n [2, -2, 2, 2, 2]], determine the sum of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 318400 | MATH |
[
{
"content": "What is the sum of all entries of the matrix A^4 where A is:\n[[-5, -2, 1, 5, 2],\n [1, -3, -2, 1, 2],\n [1, 0, 3, 3, 5],\n [1, 2, 0, -5, -5],\n [0, -4, 2, -5, -4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -1602 | MATH |
[
{
"content": "Find the value at position (2, 2) of the 4th power of the matrix:\n[[2, 2, 2, -4, -2],\n [2, 1, 1, -2, 0],\n [2, 1, -2, 0, 0],\n [-4, -2, 0, -5, -2],\n [-2, 0, 0, -2, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 365 | MATH |
[
{
"content": "Find the value at position (3, 5) of the 5th power of the matrix:\n[[-5, 2, -4, 1, 5],\n [3, 0, -4, -4, 3],\n [4, 2, 3, -2, -2],\n [-4, 4, -5, 4, -2],\n [4, 4, 5, 2, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 190 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[5, 2, 0, -2, -2],\n [2, 3, -2, 0, 3],\n [0, -2, 3, 0, -2],\n [-2, 0, 0, -3, -5],\n [-2, 3, -2, -5, 4]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 265062 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the sum of absolute values of all entries of the result:\nA =\n[[2, 2, 2, -3, 0],\n [1, 3, -1, 3, 0],\n [4, 4, 4, -2, -5],\n [-5, 4, -1, -3, -1],\n [-1, -5, 2, -1, -1]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 15199 | MATH |
[
{
"content": "Find the value at position (2, 2) of the 4th power of the matrix:\n[[3, -2, 0, -2, 2],\n [-2, -5, -2, 1, -2],\n [0, -2, 5, 0, -2],\n [-2, 1, 0, 0, 0],\n [2, -2, -2, 0, 5]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1465 | MATH |
[
{
"content": "Find the value at position (4, 4) of the 4th power of the matrix:\n[[5, 3, 0, 0, 2],\n [3, -2, 4, -1, 2],\n [0, 4, -1, 3, 2],\n [0, -1, 3, -5, 0],\n [2, 2, 2, 0, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 2095 | MATH |
[
{
"content": "For the matrix power A^5 where A =\n[[4, 0, -2, 4, 2],\n [0, 1, -4, 0, 0],\n [-2, -4, -2, -2, 3],\n [4, 0, -2, -3, 2],\n [2, 0, 3, 2, -3]], determine the sum of absolute values of all entries.\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 170589 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^4 where A is:\n[[-1, 2, -2, 4, -4],\n [-2, -4, -3, -2, -2],\n [4, 3, 4, 0, 3],\n [-2, 3, 5, 3, 0],\n [-1, -3, -1, -3, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 3288 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[-1, -2, -1, 0, -2],\n [-2, -2, 3, -3, -1],\n [-1, 3, -5, -1, -2],\n [0, -3, -1, 1, 0],\n [-2, -1, -2, 0, -1]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 58997 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (4, 3) of the result:\nA =\n[[5, 2, -1, 5, -1],\n [-5, 0, -2, -3, 0],\n [-4, 2, -5, 3, 2],\n [-5, 4, 3, -4, -3],\n [-4, 2, -4, 4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 1113 | MATH |
[
{
"content": "Find the sum of absolute values of all entries of the 4th power of the matrix:\n[[-5, 0, -3, 2, -2],\n [0, -3, -3, -2, 1],\n [-3, -3, -4, 0, -2],\n [2, -2, 0, -3, -4],\n [-2, 1, -2, -4, -4]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 38875 | MATH |
[
{
"content": "What is the sum of absolute values of all entries of the matrix A^5 where A is:\n[[4, -4, -3, 2, 0],\n [-4, 3, -2, 4, -2],\n [-3, -2, 3, -1, 0],\n [2, 4, -1, -2, -2],\n [0, -2, 0, -2, 3]]?\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 182287 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (4, 3) of the result:\nA =\n[[1, 2, -2, -2, 1],\n [2, 5, -1, 0, -2],\n [-2, -1, 4, 0, 0],\n [-2, 0, 0, -5, -4],\n [1, -2, 0, -4, 0]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | 164 | MATH |
[
{
"content": "Calculate the matrix power A^4 and find the value at position (4, 1) of the result:\nA =\n[[-3, -3, -2, -2, 1],\n [-3, 2, 2, 5, 1],\n [-4, -1, 0, 4, -2],\n [4, -1, 3, 5, 1],\n [-4, 5, -5, -4, -3]]\n\nPresent the answer in LaTex format: \\boxed{Your answer}",
"role": "user"
}
] | -370 | MATH |
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